I was kind of in my second primary school, but not in any overt, targeting way - there were just some bully-type people I just didn't feel safe around. I don't seem to recall any incidents of bullying at my first primary school or even in high school but I've seen it happen to other people at all the schools I've been to.
And Mao, I don't think the problem is much better at private schools. Remember the YouTube bullying awhile ago when some kid was dumped in a bin? Weren't they from Xavier or something? And I read in the Herald Sun that some all-girls' schools have "Slap Day" or something, where they just all single out a student to slap for whatever reason whenever a teacher's back is turned. Really, there are some mean people from all over, the only difference is the level of sophistication in which the meanness is expressed.